2C+Hyperbolas,+Cubics,+and+Exponentials

Hyperbolas, Cubic functions,Exponential functions, and their parent graphs.  =Hyperbolas=

Graphing Equation math y=a(\frac{1}{x-h})+k math -**'h'** is the x asymptote -**'k'** is the y asymptote -**'a'** is how close/far away the graph is from the point at which the asymptotes intersect

__**Example #1**__


 * Graphing Form:**

math y=4(\frac{1}{x+4})+0 math

'**a'** is equal to 4 '**h'** is equal to -4 The **'a'** moved the the graph further from the key point. The **'h'** moved the graph 4 points more to the left. The **'k'** didn't move the graph. x=-4 and y=0 To determine the asymptotes you look a the graphing form of the equation. The asymptotes are the **//h//** and //**k**// in the equation
 * 'k'** is equal to 0
 * Key point** =(-4,0) This is where the asymptotes intersect each other.
 * Domain** = (-oo, -4) and (-4, oo)
 * Range** = (-oo, 0) and (0, oo)
 * Asymptotes**

__**Examples #2 and #3**__

 =**Cubic Functions**=



__**Infle****ction Point**__ - Where the graph changes from up to down. It's basically the vertex point, but because of the type of equation it is and how the graph looks, it's called an inflection point.

math y = a(x-h)^3+k math

'**h'** determines the //x//-coordinate of the inflection point.
 * 'a'** determines how far away from the inflection point the graph goes.
 * 'k'** determines the //y//-coordinate of the inflection point.

 =Exponential Functions=

math f(x)=a(k^x-h) math


 * 'k'** is the initial value
 * 'a'** is the steepness/flatness of the graph
 * '-h'** is the asymptote

This is an example of the **parent graph** for exponential functions.